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Copy pathIONISE_module_MH.R
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IONISE_module_MH.R
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library(deSolve)
library(MASS)
library(mvtnorm)
library(dplyr)
library(invgamma)
library(ramcmc)
MH.delay1.ABC <- function(P,S,rep, R_true, R_curr, sd_list, tun, S_init, E_init, I_init, R_init,
beta_param, delayparam2, pri.shape, pri.scale, maxT, flatpri = FALSE, lowbnds = c(0,0),
noiseType, noise_multi, noise_const, dist_type) {
count = 0
repeat{
u = mvrnorm(1,c(0,0),diag(c(tun[1],tun[2])))
P.star = P + S%*%u
# if(P.star[1]>1 && P.star[2]>0){
# break
# }
if(P.star[1]>lowbnds[1] && P.star[2]>lowbnds[2]){
break
}
}
timespan0 = 0:maxT
h = timespan0[2] - timespan0[1]
dd = get_divisor_dist(c(delayparam2, P.star), dist_type = dist_type)
ext_tspan = seq(from = 0, to = max(timespan0), by = h/dd)
subseq0 = round(seq(from = 1, to = dd * max(timespan0)/h + 1, by = dd))
sim_cand_ext = mean_trajectory_SEIR_dist_input(timespan = ext_tspan, theta = c(beta_param, P.star, delayparam2), y_init = c(S_init, E_init, I_init, R_init), dist_type = dist_type)
R_cand = sim_cand_ext$Rt[subseq0]
if(noiseType == 1){
sd_list_curr = noise_multi * sqrt(R_true - R_init) + noise_const
sd_list_cand = sd_list_curr
}else if(noiseType == 2){
sd_list_curr = noise_multi * sqrt(diff(R_true)) + noise_const
sd_list_curr = c(sd_list_curr[1] , sd_list_curr)
sd_list_cand = sd_list_curr
}else if(noiseType == 3){
sd_list_curr = noise_multi * sqrt(R_curr - R_init) + noise_const
sd_list_cand = noise_multi * sqrt(R_cand - R_init) + noise_const
}else{
sd_list_curr = noise_multi * sqrt(diff(R_curr)) + noise_const
sd_list_curr = c(sd_list_curr[1] , sd_list_curr)
sd_list_cand = noise_multi * sqrt(diff(R_cand)) + noise_const
sd_list_cand = c(sd_list_cand[1] , sd_list_cand)
}
l_lik_curr = sum(dnorm(R_curr, mean = R_true, sd = sd_list_curr, log = TRUE))
l_lik_cand = sum(dnorm(R_cand, mean = R_true, sd = sd_list_cand, log = TRUE))
l.prior1.st <- dgamma(P.star[1], shape = pri.shape[1], rate = pri.shape[2], log = TRUE)
l.prior1 <- dgamma(P[1] , shape = pri.shape[1], rate = pri.shape[2], log = TRUE)
l.prior2.st <- dgamma(P.star[2], shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
l.prior2 <- dgamma(P[2] , shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
if(flatpri){
logMH <- (l_lik_cand - l_lik_curr
+ log(pmvnorm(upper = c(P[1] - lowbnds[1],P[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1])
- log(pmvnorm(upper = c(P.star[1] - lowbnds[1],P.star[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1]))
}else{
logMH <- (l_lik_cand - l_lik_curr + l.prior1.st - l.prior1 + l.prior2.st - l.prior2
+ log(pmvnorm(upper = c(P[1] - lowbnds[1],P[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1])
- log(pmvnorm(upper = c(P.star[1] - lowbnds[1],P.star[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1]))
}
alpha = min (exp(logMH),1)
if(!is.nan(alpha) && runif(1)<alpha){
P <- P.star
count = 1
R_curr = R_cand
}
S.update=ramcmc::adapt_S(S,u,alpha,rep,gamma = min(1,(2*rep)^(-1)))
if(is.nan(min(S.update))) S.update=S
S.update=(S.update+S)/2;
return(list(P=P, S=S.update, count=count, R_new = R_curr))
}
MH.delay1.ABC.pois <- function(P,S,rep, R_true, R_curr, tun, S_init, E_init, I_init, R_init,
beta_param, delayparam2, pri.shape, pri.scale, maxT, flatpri = FALSE, lowbnds = c(0,0), dist_type) {
count = 0
repeat{
u = mvrnorm(1,c(0,0),diag(c(tun[1],tun[2])))
P.star = P + S%*%u
# if(P.star[1]>1 && P.star[2]>0){
# break
# }
if(P.star[1]>lowbnds[1] && P.star[2]>lowbnds[2]){
break
}
}
timespan0 = 0:maxT
h = timespan0[2] - timespan0[1]
dd = get_divisor_dist(c(delayparam2, P.star), dist_type = dist_type)
ext_tspan = seq(from = 0, to = max(timespan0), by = h/dd)
subseq0 = round(seq(from = 1, to = dd * max(timespan0)/h + 1, by = dd))
sim_cand_ext = mean_trajectory_SEIR_dist_input(timespan = ext_tspan, theta = c(beta_param, P.star, delayparam2), y_init = c(S_init, E_init, I_init, R_init), dist_type = dist_type)
R_cand = sim_cand_ext$Rt[subseq0]
l_lik_curr = sum(dpois(R_true, lambda = R_curr, log = TRUE))
l_lik_cand = sum(dpois(R_true, lambda = R_cand, log = TRUE))
l.prior1.st <- dgamma(P.star[1], shape = pri.shape[1], rate = pri.shape[2], log = TRUE)
l.prior1 <- dgamma(P[1] , shape = pri.shape[1], rate = pri.shape[2], log = TRUE)
l.prior2.st <- dgamma(P.star[2], shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
l.prior2 <- dgamma(P[2] , shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
if(flatpri){
logMH <- (l_lik_cand - l_lik_curr
+ log(pmvnorm(upper = c(P[1] - lowbnds[1],P[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1])
- log(pmvnorm(upper = c(P.star[1] - lowbnds[1],P.star[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1]))
}else{
logMH <- (l_lik_cand - l_lik_curr + l.prior1.st - l.prior1 + l.prior2.st - l.prior2
+ log(pmvnorm(upper = c(P[1] - lowbnds[1],P[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1])
- log(pmvnorm(upper = c(P.star[1] - lowbnds[1],P.star[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1]))
}
alpha = min (exp(logMH),1)
if(!is.nan(alpha) && runif(1)<alpha){
P <- P.star
count = 1
R_curr = R_cand
}
S.update=ramcmc::adapt_S(S,u,alpha,rep,gamma = min(1,(2*rep)^(-1)))
if(is.nan(min(S.update))) S.update=S
S.update=(S.update+S)/2;
return(list(P=P, S=S.update, count=count, R_new = R_curr))
}
MH.delay2.ABC <- function(P,S,rep, R_true, R_curr, sd_list, tun, S_init, E_init, I_init, R_init,
beta_param, delayparam1, pri.shape, pri.scale, maxT, flatpri = FALSE, lowbnds = c(0,0),
noiseType, noise_multi, noise_const, dist_type = dist_type) {
count = 0
repeat{
u = mvrnorm(1,c(0,0),diag(c(tun[1],tun[2])))
P.star = P + S%*%u
# if(P.star[1]>1 && P.star[2]>0){
# break
# }
if(P.star[1]>lowbnds[1] && P.star[2]>lowbnds[2]){
break
}
}
timespan0 = 0:maxT
h = timespan0[2] - timespan0[1]
dd = get_divisor_dist(c(delayparam1, P.star), dist_type = dist_type)
ext_tspan = seq(from = 0, to = max(timespan0), by = h/dd)
subseq0 = round(seq(from = 1, to = dd * max(timespan0)/h + 1, by = dd))
sim_cand_ext = mean_trajectory_SEIR_dist_input(timespan = ext_tspan, theta = c(beta_param, delayparam1, P.star), y_init = c(S_init, E_init, I_init, R_init), dist_type = dist_type)
R_cand = sim_cand_ext$Rt[subseq0]
if(noiseType == 1){
sd_list_curr = noise_multi * sqrt(R_true - R_init) + noise_const
sd_list_cand = sd_list_curr
}else if(noiseType == 2){
sd_list_curr = noise_multi * sqrt(diff(R_true)) + noise_const
sd_list_curr = c(sd_list_curr[1] , sd_list_curr)
sd_list_cand = sd_list_curr
}else if(noiseType == 3){
sd_list_curr = noise_multi * sqrt(R_curr - R_init) + noise_const
sd_list_cand = noise_multi * sqrt(R_cand - R_init) + noise_const
}else{
sd_list_curr = noise_multi * sqrt(diff(R_curr)) + noise_const
sd_list_curr = c(sd_list_curr[1] , sd_list_curr)
sd_list_cand = noise_multi * sqrt(diff(R_cand)) + noise_const
sd_list_cand = c(sd_list_cand[1] , sd_list_cand)
}
l_lik_curr = sum(dnorm(R_curr, mean = R_true, sd = sd_list_curr, log = TRUE))
l_lik_cand = sum(dnorm(R_cand, mean = R_true, sd = sd_list_cand, log = TRUE))
l.prior1.st <- dgamma(P.star[1], shape = pri.shape[1], rate = pri.shape[2], log = TRUE)
l.prior1 <- dgamma(P[1] , shape = pri.shape[1], rate = pri.shape[2], log = TRUE)
l.prior2.st <- dgamma(P.star[2], shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
l.prior2 <- dgamma(P[2] , shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
if(flatpri){
logMH <- (l_lik_cand - l_lik_curr
+ log(pmvnorm(upper = c(P[1] - lowbnds[1],P[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1])
- log(pmvnorm(upper = c(P.star[1] - lowbnds[1],P.star[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1]))
}else{
logMH <- (l_lik_cand - l_lik_curr + l.prior1.st - l.prior1 + l.prior2.st - l.prior2
+ log(pmvnorm(upper = c(P[1] - lowbnds[1],P[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1])
- log(pmvnorm(upper = c(P.star[1] - lowbnds[1],P.star[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1]))
}
alpha = min (exp(logMH),1)
if(!is.nan(alpha) && runif(1)<alpha){
P <- P.star
count = 1
R_curr = R_cand
}
S.update=ramcmc::adapt_S(S,u,alpha,rep,gamma = min(1,(2*rep)^(-1)))
if(is.nan(min(S.update))) S.update=S
S.update=(S.update+S)/2;
return(list(P=P, S=S.update, count=count, R_new = R_curr))
}
MH.delay2.ABC.pois <- function(P,S,rep, R_true, R_curr, tun, S_init, E_init, I_init, R_init,
beta_param, delayparam1, pri.shape, pri.scale, maxT, flatpri = FALSE, lowbnds = c(0,0), dist_type) {
count = 0
repeat{
u = mvrnorm(1,c(0,0),diag(c(tun[1],tun[2])))
P.star = P + S%*%u
# if(P.star[1]>1 && P.star[2]>0){
# break
# }
if(P.star[1]>lowbnds[1] && P.star[2]>lowbnds[2]){
break
}
}
timespan0 = 0:maxT
h = timespan0[2] - timespan0[1]
dd = get_divisor_dist(c(delayparam1, P.star), dist_type = dist_type)
ext_tspan = seq(from = 0, to = max(timespan0), by = h/dd)
subseq0 = round(seq(from = 1, to = dd * max(timespan0)/h + 1, by = dd))
sim_cand_ext = mean_trajectory_SEIR_dist_input(timespan = ext_tspan, theta = c(beta_param, delayparam1, P.star), y_init = c(S_init, E_init, I_init, R_init), dist_type = dist_type)
R_cand = sim_cand_ext$Rt[subseq0]
l_lik_curr = sum(dpois(R_true, lambda = R_curr, log = TRUE))
l_lik_cand = sum(dpois(R_true, lambda = R_cand, log = TRUE))
l.prior1.st <- dgamma(P.star[1], shape = pri.shape[1], rate = pri.shape[2], log = TRUE)
l.prior1 <- dgamma(P[1] , shape = pri.shape[1], rate = pri.shape[2], log = TRUE)
l.prior2.st <- dgamma(P.star[2], shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
l.prior2 <- dgamma(P[2] , shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
if(flatpri){
logMH <- (l_lik_cand - l_lik_curr
+ log(pmvnorm(upper = c(P[1] - lowbnds[1],P[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1])
- log(pmvnorm(upper = c(P.star[1] - lowbnds[1],P.star[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1]))
}else{
logMH <- (l_lik_cand - l_lik_curr + l.prior1.st - l.prior1 + l.prior2.st - l.prior2
+ log(pmvnorm(upper = c(P[1] - lowbnds[1],P[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1])
- log(pmvnorm(upper = c(P.star[1] - lowbnds[1],P.star[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1]))
}
alpha = min (exp(logMH),1)
if(!is.nan(alpha) && runif(1)<alpha){
P <- P.star
count = 1
R_curr = R_cand
}
S.update=ramcmc::adapt_S(S,u,alpha,rep,gamma = min(1,(2*rep)^(-1)))
if(is.nan(min(S.update))) S.update=S
S.update=(S.update+S)/2;
return(list(P=P, S=S.update, count=count, R_new = R_curr))
}
MH.delay1.ABC.exp <- function(P,S,rep, R_true, R_curr, sd_list, tun, S_init, E_init, I_init, R_init,
beta_param, delayparam2, pri.shape, pri.scale, maxT, flatpri = FALSE, lowbnds = c(0,0),
noiseType, noise_multi, noise_const){
count = 0
repeat{
u = rnorm(1, 0 ,tun[2])
P.star = P + S*u
# if(P.star[1]>1 && P.star[2]>0){
# break
# }
if(P.star>lowbnds[2]){
break
}
}
timespan0 = 0:maxT
init = c(S=S_init, E1 = E_init, I1 = I_init, R = R_init)
theta_ode <- c(beta = beta_param, s1 = P.star^(-1), s2 = delayparam2[2]^(-1), N = sum(init))
sol = ode(y = init, times=timespan0, func=SEIR11, parms = theta_ode)
R_cand = sol[, dim(sol)[2]]
if(noiseType == 1){
sd_list_curr = noise_multi * sqrt(R_true - R_init) + noise_const
sd_list_cand = sd_list_curr
}else if(noiseType == 2){
sd_list_curr = noise_multi * sqrt(diff(R_true)) + noise_const
sd_list_curr = c(sd_list_curr[1] , sd_list_curr)
sd_list_cand = sd_list_curr
}else if(noiseType == 3){
sd_list_curr = noise_multi * sqrt(R_curr - R_init) + noise_const
sd_list_cand = noise_multi * sqrt(R_cand - R_init) + noise_const
}else{
sd_list_curr = noise_multi * sqrt(diff(R_curr)) + noise_const
sd_list_curr = c(sd_list_curr[1] , sd_list_curr)
sd_list_cand = noise_multi * sqrt(diff(R_cand)) + noise_const
sd_list_cand = c(sd_list_cand[1] , sd_list_cand)
}
l_lik_curr = sum(dnorm(R_curr, mean = R_true, sd = sd_list_curr, log = TRUE))
l_lik_cand = sum(dnorm(R_cand, mean = R_true, sd = sd_list_cand, log = TRUE))
l.prior2.st <- dgamma(P.star, shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
l.prior2 <- dgamma(P , shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
if(flatpri){
logMH <- (l_lik_cand - l_lik_curr
+ log(pnorm(P - lowbnds[2], sd = S*sqrt(tun[2])))
- log(pnorm(P.star - lowbnds[2], sd = S*sqrt(tun[2]))))
}else{
logMH <- (l_lik_cand - l_lik_curr + l.prior2.st - l.prior2
+ log(pnorm(P - lowbnds[2], sd = S*sqrt(tun[2])))
- log(pnorm(P.star - lowbnds[2], sd = S*sqrt(tun[2]))))
}
alpha = min (exp(logMH),1)
if(!is.nan(alpha) && runif(1)<alpha){
P <- P.star
count = 1
R_curr = R_cand
}
S.update=ramcmc::adapt_S(S,u,alpha,rep,gamma = min(1,(2*rep)^(-1)))
if(is.nan(min(S.update))) S.update=S
S.update=(S.update+S)/2;
return(list(P=P, S=S.update, count=count, R_new = R_curr))
}
MH.delay1.ABC.exp.pois <- function(P,S,rep, R_true, R_curr, tun, S_init, E_init, I_init, R_init,
beta_param, delayparam2, pri.shape, pri.scale, maxT, flatpri = FALSE, lowbnds = c(0,0)){
count = 0
repeat{
u = rnorm(1, 0 ,tun[2])
P.star = P + S*u
# if(P.star[1]>1 && P.star[2]>0){
# break
# }
if(P.star>lowbnds[2]){
break
}
}
timespan0 = 0:maxT
init = c(S=S_init, E1 = E_init, I1 = I_init, R = R_init)
theta_ode <- c(beta = beta_param, s1 = P.star^(-1), s2 = delayparam2[2]^(-1), N = sum(init))
sol = ode(y = init, times=timespan0, func=SEIR11, parms = theta_ode)
R_cand = sol[, dim(sol)[2]]
l_lik_curr = sum(dpois(R_true, lambda = R_curr, log = TRUE))
l_lik_cand = sum(dpois(R_true, lambda = R_cand, log = TRUE))
l.prior2.st <- dgamma(P.star, shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
l.prior2 <- dgamma(P , shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
if(flatpri){
logMH <- (l_lik_cand - l_lik_curr
+ log(pnorm(P - lowbnds[2], sd = S*sqrt(tun[2])))
- log(pnorm(P.star - lowbnds[2], sd = S*sqrt(tun[2]))))
}else{
logMH <- (l_lik_cand - l_lik_curr + l.prior2.st - l.prior2
+ log(pnorm(P - lowbnds[2], sd = S*sqrt(tun[2])))
- log(pnorm(P.star - lowbnds[2], sd = S*sqrt(tun[2]))))
}
alpha = min (exp(logMH),1)
if(!is.nan(alpha) && runif(1)<alpha){
P <- P.star
count = 1
R_curr = R_cand
}
S.update=ramcmc::adapt_S(S,u,alpha,rep,gamma = min(1,(2*rep)^(-1)))
if(is.nan(min(S.update))) S.update=S
S.update=(S.update+S)/2;
return(list(P=P, S=S.update, count=count, R_new = R_curr))
}
MH.delay2.ABC.exp <- function(P,S,rep, R_true, R_curr, sd_list, tun, S_init, E_init, I_init, R_init,
beta_param, delayparam1, pri.shape, pri.scale, maxT, flatpri = FALSE, lowbnds = c(0,0),
noiseType, noise_multi, noise_const) {
count = 0
repeat{
u = rnorm(1, 0 ,tun[2])
P.star = P + S*u
# if(P.star[1]>1 && P.star[2]>0){
# break
# }
if(P.star>lowbnds[2]){
break
}
}
timespan0 = 0:maxT
init = c(S=S_init, E1 = E_init, I1 = I_init, R = R_init)
theta_ode <- c(beta = beta_param, s1 = delayparam1[2]^(-1), s2 = P.star^(-1), N = sum(init))
sol = ode(y = init, times=timespan0, func=SEIR11, parms = theta_ode)
R_cand = sol[, dim(sol)[2]]
if(noiseType == 1){
sd_list_curr = noise_multi * sqrt(R_true - R_init) + noise_const
sd_list_cand = sd_list_curr
}else if(noiseType == 2){
sd_list_curr = noise_multi * sqrt(diff(R_true)) + noise_const
sd_list_curr = c(sd_list_curr[1] , sd_list_curr)
sd_list_cand = sd_list_curr
}else if(noiseType == 3){
sd_list_curr = noise_multi * sqrt(R_curr - R_init) + noise_const
sd_list_cand = noise_multi * sqrt(R_cand - R_init) + noise_const
}else{
sd_list_curr = noise_multi * sqrt(diff(R_curr)) + noise_const
sd_list_curr = c(sd_list_curr[1] , sd_list_curr)
sd_list_cand = noise_multi * sqrt(diff(R_cand)) + noise_const
sd_list_cand = c(sd_list_cand[1] , sd_list_cand)
}
l_lik_curr = sum(dnorm(R_curr, mean = R_true, sd = sd_list_curr, log = TRUE))
l_lik_cand = sum(dnorm(R_cand, mean = R_true, sd = sd_list_cand, log = TRUE))
l.prior2.st <- dgamma(P.star, shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
l.prior2 <- dgamma(P , shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
if(flatpri){
logMH <- (l_lik_cand - l_lik_curr
+ log(pnorm(P - lowbnds[2], sd = S*sqrt(tun[2])))
- log(pnorm(P.star - lowbnds[2], sd = S*sqrt(tun[2]))))
}else{
logMH <- (l_lik_cand - l_lik_curr + l.prior2.st - l.prior2
+ log(pnorm(P - lowbnds[2], sd = S*sqrt(tun[2])))
- log(pnorm(P.star - lowbnds[2], sd = S*sqrt(tun[2]))))
}
alpha = min (exp(logMH),1)
if(!is.nan(alpha) && runif(1)<alpha){
P <- P.star
count = 1
R_curr = R_cand
}
S.update=ramcmc::adapt_S(S,u,alpha,rep,gamma = min(1,(2*rep)^(-1)))
if(is.nan(min(S.update))) S.update=S
S.update=(S.update+S)/2;
return(list(P=P, S=S.update, count=count, R_new = R_curr))
}
MH.delay2.ABC.exp.pois <- function(P,S,rep, R_true, R_curr, tun, S_init, E_init, I_init, R_init,
beta_param, delayparam1, pri.shape, pri.scale, maxT, flatpri = FALSE, lowbnds = c(0,0)) {
count = 0
repeat{
u = rnorm(1, 0 ,tun[2])
P.star = P + S*u
# if(P.star[1]>1 && P.star[2]>0){
# break
# }
if(P.star>lowbnds[2]){
break
}
}
timespan0 = 0:maxT
init = c(S=S_init, E1 = E_init, I1 = I_init, R = R_init)
theta_ode <- c(beta = beta_param, s1 = delayparam1[2]^(-1), s2 = P.star^(-1), N = sum(init))
sol = ode(y = init, times=timespan0, func=SEIR11, parms = theta_ode)
R_cand = sol[, dim(sol)[2]]
l_lik_curr = sum(dpois(R_true, lambda = R_curr, log = TRUE))
l_lik_cand = sum(dpois(R_true, lambda = R_cand, log = TRUE))
l.prior2.st <- dgamma(P.star, shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
l.prior2 <- dgamma(P , shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
if(flatpri){
logMH <- (l_lik_cand - l_lik_curr
+ log(pnorm(P - lowbnds[2], sd = S*sqrt(tun[2])))
- log(pnorm(P.star - lowbnds[2], sd = S*sqrt(tun[2]))))
}else{
logMH <- (l_lik_cand - l_lik_curr + l.prior2.st - l.prior2
+ log(pnorm(P - lowbnds[2], sd = S*sqrt(tun[2])))
- log(pnorm(P.star - lowbnds[2], sd = S*sqrt(tun[2]))))
}
alpha = min (exp(logMH),1)
if(!is.nan(alpha) && runif(1)<alpha){
P <- P.star
count = 1
R_curr = R_cand
}
S.update=ramcmc::adapt_S(S,u,alpha,rep,gamma = min(1,(2*rep)^(-1)))
if(is.nan(min(S.update))) S.update=S
S.update=(S.update+S)/2;
return(list(P=P, S=S.update, count=count, R_new = R_curr))
}
MH.delay1.ABC.hist <- function(P,S,rep, R_true, R_curr, sd_list, tun, S_init, E_init, I_init, R_init,
beta_param, delayparam2, pri.shape, pri.scale, maxT, flatpri = FALSE, lowbnds = c(0,0),
noiseType, noise_multi, noise_const) {
count = 0
repeat{
u = mvrnorm(1,c(0,0),diag(c(tun[1],tun[2])))
P.star = P + S%*%u
# if(P.star[1]>1 && P.star[2]>0){
# break
# }
if(P.star[1]>lowbnds[1] && P.star[2]>lowbnds[2]){
break
}
}
timespan0 = 0:maxT
h = timespan0[2] - timespan0[1]
dd = get_divisor_dist(c(delayparam2, P.star), dist_type = "gamma")
ext_tspan = seq(from = 0, to = max(timespan0), by = h/dd)
subseq0 = round(seq(from = 1, to = dd * max(timespan0)/h + 1, by = dd))
sim_cand_ext = mean_trajectory_SEIR_hist(timespan = ext_tspan, theta = c(beta_param, P.star, delayparam2), y_init = c(S_init, E_init, I_init, R_init))
R_cand = sim_cand_ext$Rt[subseq0]
if(noiseType == 1){
sd_list_curr = noise_multi * sqrt(R_true - R_init) + noise_const
sd_list_cand = sd_list_curr
}else if(noiseType == 2){
sd_list_curr = noise_multi * sqrt(diff(R_true)) + noise_const
sd_list_curr = c(sd_list_curr[1] , sd_list_curr)
sd_list_cand = sd_list_curr
}else if(noiseType == 3){
sd_list_curr = noise_multi * sqrt(R_curr - R_init) + noise_const
sd_list_cand = noise_multi * sqrt(R_cand - R_init) + noise_const
}else{
sd_list_curr = noise_multi * sqrt(diff(R_curr)) + noise_const
sd_list_curr = c(sd_list_curr[1] , sd_list_curr)
sd_list_cand = noise_multi * sqrt(diff(R_cand)) + noise_const
sd_list_cand = c(sd_list_cand[1] , sd_list_cand)
}
l_lik_curr = sum(dnorm(R_curr, mean = R_true, sd = sd_list_curr, log = TRUE))
l_lik_cand = sum(dnorm(R_cand, mean = R_true, sd = sd_list_cand, log = TRUE))
l.prior1.st <- dgamma(P.star[1], shape = pri.shape[1], rate = pri.shape[2], log = TRUE)
l.prior1 <- dgamma(P[1] , shape = pri.shape[1], rate = pri.shape[2], log = TRUE)
l.prior2.st <- dgamma(P.star[2], shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
l.prior2 <- dgamma(P[2] , shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
if(flatpri){
logMH <- (l_lik_cand - l_lik_curr
+ log(pmvnorm(upper = c(P[1] - lowbnds[1],P[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1])
- log(pmvnorm(upper = c(P.star[1] - lowbnds[1],P.star[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1]))
}else{
logMH <- (l_lik_cand - l_lik_curr + l.prior1.st - l.prior1 + l.prior2.st - l.prior2
+ log(pmvnorm(upper = c(P[1] - lowbnds[1],P[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1])
- log(pmvnorm(upper = c(P.star[1] - lowbnds[1],P.star[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1]))
}
alpha = min (exp(logMH),1)
if(!is.nan(alpha) && runif(1)<alpha){
P <- P.star
count = 1
R_curr = R_cand
}
S.update=ramcmc::adapt_S(S,u,alpha,rep,gamma = min(1,(2*rep)^(-1)))
if(is.nan(min(S.update))) S.update=S
S.update=(S.update+S)/2;
return(list(P=P, S=S.update, count=count, R_new = R_curr))
}
MH.delay1.ABC.pois.hist <- function(P,S,rep, R_true, R_curr, tun, S_init, E_init, I_init, R_init,
beta_param, delayparam2, pri.shape, pri.scale, maxT, flatpri = FALSE, lowbnds = c(0,0)) {
count = 0
repeat{
u = mvrnorm(1,c(0,0),diag(c(tun[1],tun[2])))
P.star = P + S%*%u
# if(P.star[1]>1 && P.star[2]>0){
# break
# }
if(P.star[1]>lowbnds[1] && P.star[2]>lowbnds[2]){
break
}
}
timespan0 = 0:maxT
h = timespan0[2] - timespan0[1]
dd = get_divisor_dist(c(delayparam2, P.star), dist_type = "gamma")
ext_tspan = seq(from = 0, to = max(timespan0), by = h/dd)
subseq0 = round(seq(from = 1, to = dd * max(timespan0)/h + 1, by = dd))
sim_cand_ext = mean_trajectory_SEIR_hist(timespan = ext_tspan, theta = c(beta_param, P.star, delayparam2), y_init = c(S_init, E_init, I_init, R_init))
R_cand = sim_cand_ext$Rt[subseq0]
l_lik_curr = sum(dpois(R_true, lambda = R_curr, log = TRUE))
l_lik_cand = sum(dpois(R_true, lambda = R_cand, log = TRUE))
l.prior1.st <- dgamma(P.star[1], shape = pri.shape[1], rate = pri.shape[2], log = TRUE)
l.prior1 <- dgamma(P[1] , shape = pri.shape[1], rate = pri.shape[2], log = TRUE)
l.prior2.st <- dgamma(P.star[2], shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
l.prior2 <- dgamma(P[2] , shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
if(flatpri){
logMH <- (l_lik_cand - l_lik_curr
+ log(pmvnorm(upper = c(P[1] - lowbnds[1],P[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1])
- log(pmvnorm(upper = c(P.star[1] - lowbnds[1],P.star[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1]))
}else{
logMH <- (l_lik_cand - l_lik_curr + l.prior1.st - l.prior1 + l.prior2.st - l.prior2
+ log(pmvnorm(upper = c(P[1] - lowbnds[1],P[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1])
- log(pmvnorm(upper = c(P.star[1] - lowbnds[1],P.star[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1]))
}
alpha = min (exp(logMH),1)
if(!is.nan(alpha) && runif(1)<alpha){
P <- P.star
count = 1
R_curr = R_cand
}
S.update=ramcmc::adapt_S(S,u,alpha,rep,gamma = min(1,(2*rep)^(-1)))
if(is.nan(min(S.update))) S.update=S
S.update=(S.update+S)/2;
return(list(P=P, S=S.update, count=count, R_new = R_curr))
}
MH.delay2.ABC.hist <- function(P,S,rep, R_true, R_curr, sd_list, tun, S_init, E_init, I_init, R_init,
beta_param, delayparam1, pri.shape, pri.scale, maxT, flatpri = FALSE, lowbnds = c(0,0),
noiseType, noise_multi, noise_const) {
count = 0
lowbnds = c(1.1, 0.1)
repeat{
u = mvrnorm(1,c(0,0),diag(c(tun[1],tun[2])))
P.star = P + S%*%u
# if(P.star[1]>1 && P.star[2]>0){
# break
# }
if(P.star[1]>lowbnds[1] && P.star[2]>lowbnds[2]){
break
}
}
timespan0 = 0:maxT
h = timespan0[2] - timespan0[1]
dd = get_divisor_dist(c(delayparam1, P.star), dist_type = "gamma")
ext_tspan = seq(from = 0, to = max(timespan0), by = h/dd)
subseq0 = round(seq(from = 1, to = dd * max(timespan0)/h + 1, by = dd))
sim_cand_ext = mean_trajectory_SEIR_hist(timespan = ext_tspan, theta = c(beta_param, delayparam1, P.star), y_init = c(S_init, E_init, I_init, R_init))
R_cand = sim_cand_ext$Rt[subseq0]
if(noiseType == 1){
sd_list_curr = noise_multi * sqrt(R_true - R_init) + noise_const
sd_list_cand = sd_list_curr
}else if(noiseType == 2){
sd_list_curr = noise_multi * sqrt(diff(R_true)) + noise_const
sd_list_curr = c(sd_list_curr[1] , sd_list_curr)
sd_list_cand = sd_list_curr
}else if(noiseType == 3){
sd_list_curr = noise_multi * sqrt(R_curr - R_init) + noise_const
sd_list_cand = noise_multi * sqrt(R_cand - R_init) + noise_const
}else{
sd_list_curr = noise_multi * sqrt(diff(R_curr)) + noise_const
sd_list_curr = c(sd_list_curr[1] , sd_list_curr)
sd_list_cand = noise_multi * sqrt(diff(R_cand)) + noise_const
sd_list_cand = c(sd_list_cand[1] , sd_list_cand)
}
l_lik_curr = sum(dnorm(R_curr, mean = R_true, sd = sd_list_curr, log = TRUE))
l_lik_cand = sum(dnorm(R_cand, mean = R_true, sd = sd_list_cand, log = TRUE))
l.prior1.st <- dgamma(P.star[1], shape = pri.shape[1], rate = pri.shape[2], log = TRUE)
l.prior1 <- dgamma(P[1] , shape = pri.shape[1], rate = pri.shape[2], log = TRUE)
l.prior2.st <- dgamma(P.star[2], shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
l.prior2 <- dgamma(P[2] , shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
if(flatpri){
logMH <- (l_lik_cand - l_lik_curr
+ log(pmvnorm(upper = c(P[1] - lowbnds[1],P[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1])
- log(pmvnorm(upper = c(P.star[1] - lowbnds[1],P.star[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1]))
}else{
logMH <- (l_lik_cand - l_lik_curr + l.prior1.st - l.prior1 + l.prior2.st - l.prior2
+ log(pmvnorm(upper = c(P[1] - lowbnds[1],P[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1])
- log(pmvnorm(upper = c(P.star[1] - lowbnds[1],P.star[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1]))
}
alpha = min (exp(logMH),1)
if(!is.nan(alpha) && runif(1)<alpha){
P <- P.star
count = 1
R_curr = R_cand
}
S.update=ramcmc::adapt_S(S,u,alpha,rep,gamma = min(1,(2*rep)^(-1)))
if(is.nan(min(S.update))) S.update=S
S.update=(S.update+S)/2;
return(list(P=P, S=S.update, count=count, R_new = R_curr))
}
MH.delay2.ABC.pois.hist <- function(P,S,rep, R_true, R_curr, tun, S_init, E_init, I_init, R_init,
beta_param, delayparam1, pri.shape, pri.scale, maxT, flatpri = FALSE, lowbnds = c(0,0)){
count = 0
lowbnds = c(1.1, 0.1)
repeat{
u = mvrnorm(1,c(0,0),diag(c(tun[1],tun[2])))
P.star = P + S%*%u
# if(P.star[1]>1 && P.star[2]>0){
# break
# }
if(P.star[1]>lowbnds[1] && P.star[2]>lowbnds[2]){
break
}
}
timespan0 = 0:maxT
h = timespan0[2] - timespan0[1]
dd = get_divisor_dist(c(delayparam1, P.star), dist_type = "gamma")
ext_tspan = seq(from = 0, to = max(timespan0), by = h/dd)
subseq0 = round(seq(from = 1, to = dd * max(timespan0)/h + 1, by = dd))
sim_cand_ext = mean_trajectory_SEIR_hist(timespan = ext_tspan, theta = c(beta_param, delayparam1, P.star), y_init = c(S_init, E_init, I_init, R_init))
R_cand = sim_cand_ext$Rt[subseq0]
l_lik_curr = sum(dpois(R_true, lambda = R_curr, log = TRUE))
l_lik_cand = sum(dpois(R_true, lambda = R_cand, log = TRUE))
l.prior1.st <- dgamma(P.star[1], shape = pri.shape[1], rate = pri.shape[2], log = TRUE)
l.prior1 <- dgamma(P[1] , shape = pri.shape[1], rate = pri.shape[2], log = TRUE)
l.prior2.st <- dgamma(P.star[2], shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
l.prior2 <- dgamma(P[2] , shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
if(flatpri){
logMH <- (l_lik_cand - l_lik_curr
+ log(pmvnorm(upper = c(P[1] - lowbnds[1],P[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1])
- log(pmvnorm(upper = c(P.star[1] - lowbnds[1],P.star[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1]))
}else{
logMH <- (l_lik_cand - l_lik_curr + l.prior1.st - l.prior1 + l.prior2.st - l.prior2
+ log(pmvnorm(upper = c(P[1] - lowbnds[1],P[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1])
- log(pmvnorm(upper = c(P.star[1] - lowbnds[1],P.star[2] - lowbnds[2]), sigma = S%*%t(S)%*%diag(c(tun[1],tun[2])))[1]))
}
alpha = min (exp(logMH),1)
if(!is.nan(alpha) && runif(1)<alpha){
P <- P.star
count = 1
R_curr = R_cand
}
S.update=ramcmc::adapt_S(S,u,alpha,rep,gamma = min(1,(2*rep)^(-1)))
if(is.nan(min(S.update))) S.update=S
S.update=(S.update+S)/2;
return(list(P=P, S=S.update, count=count, R_new = R_curr))
}
MH.delay1.ABC.exp.hist <- function(P,S,rep, R_true, R_curr, sd_list, tun, S_init, E_init, I_init, R_init,
beta_param, delayparam2, pri.shape, pri.scale, maxT, flatpri = FALSE, lowbnds = c(0,0),
noiseType, noise_multi, noise_const) {
count = 0
repeat{
u = rnorm(1, 0 ,tun[2])
P.star = P + S*u
# if(P.star[1]>1 && P.star[2]>0){
# break
# }
if(P.star>lowbnds[2]){
break
}
}
timespan0 = 0:maxT
init = c(S=S_init, E1 = E_init, I1 = I_init, R = R_init)
theta_ode <- c(beta = beta_param, s1 = P.star^(-1), s2 = delayparam2[2]^(-1), N = sum(init))
sol = ode(y = init, times=timespan0, func=SEIR11, parms = theta_ode)
R_cand = sol[, dim(sol)[2]]
if(noiseType == 1){
sd_list_curr = noise_multi * sqrt(R_true - R_init) + noise_const
sd_list_cand = sd_list_curr
}else if(noiseType == 2){
sd_list_curr = noise_multi * sqrt(diff(R_true)) + noise_const
sd_list_curr = c(sd_list_curr[1] , sd_list_curr)
sd_list_cand = sd_list_curr
}else if(noiseType == 3){
sd_list_curr = noise_multi * sqrt(R_curr - R_init) + noise_const
sd_list_cand = noise_multi * sqrt(R_cand - R_init) + noise_const
}else{
sd_list_curr = noise_multi * sqrt(diff(R_curr)) + noise_const
sd_list_curr = c(sd_list_curr[1] , sd_list_curr)
sd_list_cand = noise_multi * sqrt(diff(R_cand)) + noise_const
sd_list_cand = c(sd_list_cand[1] , sd_list_cand)
}
l_lik_curr = sum(dnorm(R_curr, mean = R_true, sd = sd_list_curr, log = TRUE))
l_lik_cand = sum(dnorm(R_cand, mean = R_true, sd = sd_list_cand, log = TRUE))
l.prior2.st <- dgamma(P.star, shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
l.prior2 <- dgamma(P , shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
if(flatpri){
logMH <- (l_lik_cand - l_lik_curr
+ log(pnorm(P - lowbnds[2], sd = S*sqrt(tun[2])))
- log(pnorm(P.star - lowbnds[2], sd = S*sqrt(tun[2]))))
}else{
logMH <- (l_lik_cand - l_lik_curr + l.prior2.st - l.prior2
+ log(pnorm(P - lowbnds[2], sd = S*sqrt(tun[2])))
- log(pnorm(P.star - lowbnds[2], sd = S*sqrt(tun[2]))))
}
alpha = min (exp(logMH),1)
if(!is.nan(alpha) && runif(1)<alpha){
P <- P.star
count = 1
R_curr = R_cand
}
S.update=ramcmc::adapt_S(S,u,alpha,rep,gamma = min(1,(2*rep)^(-1)))
if(is.nan(min(S.update))) S.update=S
S.update=(S.update+S)/2;
return(list(P=P, S=S.update, count=count, R_new = R_curr))
}
MH.delay1.ABC.exp.pois.hist <- function(P,S,rep, R_true, R_curr, tun, S_init, E_init, I_init, R_init,
beta_param, delayparam2, pri.shape, pri.scale, maxT, flatpri = FALSE, lowbnds = c(0,0)) {
count = 0
repeat{
u = rnorm(1, 0 ,tun[2])
P.star = P + S*u
# if(P.star[1]>1 && P.star[2]>0){
# break
# }
if(P.star>lowbnds[2]){
break
}
}
timespan0 = 0:maxT
init = c(S=S_init, E1 = E_init, I1 = I_init, R = R_init)
theta_ode <- c(beta = beta_param, s1 = P.star^(-1), s2 = delayparam2[2]^(-1), N = sum(init))
sol = ode(y = init, times=timespan0, func=SEIR11, parms = theta_ode)
R_cand = sol[, dim(sol)[2]]
l_lik_curr = sum(dpois(R_true, lambda = R_curr, log = TRUE))
l_lik_cand = sum(dpois(R_true, lambda = R_cand, log = TRUE))
l.prior2.st <- dgamma(P.star, shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
l.prior2 <- dgamma(P , shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
if(flatpri){
logMH <- (l_lik_cand - l_lik_curr
+ log(pnorm(P - lowbnds[2], sd = S*sqrt(tun[2])))
- log(pnorm(P.star - lowbnds[2], sd = S*sqrt(tun[2]))))
}else{
logMH <- (l_lik_cand - l_lik_curr + l.prior2.st - l.prior2
+ log(pnorm(P - lowbnds[2], sd = S*sqrt(tun[2])))
- log(pnorm(P.star - lowbnds[2], sd = S*sqrt(tun[2]))))
}
alpha = min (exp(logMH),1)
if(!is.nan(alpha) && runif(1)<alpha){
P <- P.star
count = 1
R_curr = R_cand
}
S.update=ramcmc::adapt_S(S,u,alpha,rep,gamma = min(1,(2*rep)^(-1)))
if(is.nan(min(S.update))) S.update=S
S.update=(S.update+S)/2;
return(list(P=P, S=S.update, count=count, R_new = R_curr))
}
MH.delay2.ABC.exp.hist <- function(P,S,rep, R_true, R_curr, sd_list, tun, S_init, E_init, I_init, R_init,
beta_param, delayparam1, pri.shape, pri.scale, maxT, flatpri = FALSE, lowbnds = c(0,0),
noiseType, noise_multi, noise_const) {
count = 0
repeat{
u = rnorm(1, 0 ,tun[2])
P.star = P + S*u
# if(P.star[1]>1 && P.star[2]>0){
# break
# }
if(P.star>lowbnds[2]){
break
}
}
timespan0 = 0:maxT
init = c(S=S_init, E1 = E_init, I1 = I_init, R = R_init)
theta_ode <- c(beta = beta_param, s1 = delayparam1[2]^(-1), s2 = P.star^(-1), N = sum(init))
sol = ode(y = init, times=timespan0, func=SEIR11, parms = theta_ode)
R_cand = sol[, dim(sol)[2]]
if(noiseType == 1){
sd_list_curr = noise_multi * sqrt(R_true - R_init) + noise_const
sd_list_cand = sd_list_curr
}else if(noiseType == 2){
sd_list_curr = noise_multi * sqrt(diff(R_true)) + noise_const
sd_list_curr = c(sd_list_curr[1] , sd_list_curr)
sd_list_cand = sd_list_curr
}else if(noiseType == 3){
sd_list_curr = noise_multi * sqrt(R_curr - R_init) + noise_const
sd_list_cand = noise_multi * sqrt(R_cand - R_init) + noise_const
}else{
sd_list_curr = noise_multi * sqrt(diff(R_curr)) + noise_const
sd_list_curr = c(sd_list_curr[1] , sd_list_curr)
sd_list_cand = noise_multi * sqrt(diff(R_cand)) + noise_const
sd_list_cand = c(sd_list_cand[1] , sd_list_cand)
}
l_lik_curr = sum(dnorm(R_curr, mean = R_true, sd = sd_list_curr, log = TRUE))
l_lik_cand = sum(dnorm(R_cand, mean = R_true, sd = sd_list_cand, log = TRUE))
l.prior2.st <- dgamma(P.star, shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
l.prior2 <- dgamma(P , shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
if(flatpri){
logMH <- (l_lik_cand - l_lik_curr
+ log(pnorm(P - lowbnds[2], sd = S*sqrt(tun[2])))
- log(pnorm(P.star - lowbnds[2], sd = S*sqrt(tun[2]))))
}else{
logMH <- (l_lik_cand - l_lik_curr + l.prior2.st - l.prior2
+ log(pnorm(P - lowbnds[2], sd = S*sqrt(tun[2])))
- log(pnorm(P.star - lowbnds[2], sd = S*sqrt(tun[2]))))
}
alpha = min (exp(logMH),1)
if(!is.nan(alpha) && runif(1)<alpha){
P <- P.star
count = 1
R_curr = R_cand
}
S.update=ramcmc::adapt_S(S,u,alpha,rep,gamma = min(1,(2*rep)^(-1)))
if(is.nan(min(S.update))) S.update=S
S.update=(S.update+S)/2;
return(list(P=P, S=S.update, count=count, R_new = R_curr))
}
MH.delay2.ABC.exp.pois.hist <- function(P,S,rep, R_true, R_curr, tun, S_init, E_init, I_init, R_init,
beta_param, delayparam1, pri.shape, pri.scale, maxT, flatpri = FALSE, lowbnds = c(0,0)) {
count = 0
repeat{
u = rnorm(1, 0 ,tun[2])
P.star = P + S*u
# if(P.star[1]>1 && P.star[2]>0){
# break
# }
if(P.star>lowbnds[2]){
break
}
}
timespan0 = 0:maxT
init = c(S=S_init, E1 = E_init, I1 = I_init, R = R_init)
theta_ode <- c(beta = beta_param, s1 = delayparam1[2]^(-1), s2 = P.star^(-1), N = sum(init))
sol = ode(y = init, times=timespan0, func=SEIR11, parms = theta_ode)
R_cand = sol[, dim(sol)[2]]
l_lik_curr = sum(dpois(R_true, lambda = R_curr, log = TRUE))
l_lik_cand = sum(dpois(R_true, lambda = R_cand, log = TRUE))
l.prior2.st <- dgamma(P.star, shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
l.prior2 <- dgamma(P , shape = pri.scale[1], rate = pri.scale[2], log = TRUE)
if(flatpri){
logMH <- (l_lik_cand - l_lik_curr
+ log(pnorm(P - lowbnds[2], sd = S*sqrt(tun[2])))